Tree indiscernibilities, revisited

Byunghan Kim, Hyeung Joon Kim, Lynn Scow

Research output: Contribution to journalArticle

4 Citations (Scopus)

Abstract

We give definitions that distinguish between two notions of indiscernibility for a set {aη {divides} η ∈ ω>ω} that saw original use in Shelah [Classification theory and the number of non-isomorphic models (revised edition). North-Holland, Amsterdam, 1990], which we name s- and str-indiscernibility. Using these definitions and detailed proofs, we prove s- and str-modeling theorems and give applications of these theorems. In particular, we verify a step in the argument that TP is equivalent to TP1 or TP2 that has not seen explication in the literature. In the Appendix, we exposit the proofs of Shelah [Classification theory and the number of non-isomorphic models (revised edition). North-Holland, Amsterdam, 1990, App. 2.6, 2.7], expanding on the details.

Original languageEnglish
Pages (from-to)211-232
Number of pages22
JournalArchive for Mathematical Logic
Volume53
Issue number1-2
DOIs
Publication statusPublished - 2014 Feb 1

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All Science Journal Classification (ASJC) codes

  • Philosophy
  • Logic

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